Simplify the following expression: $ a = \dfrac{-10}{3q + 2} + \dfrac{-7}{6} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6}{6}$ $ \dfrac{-10}{3q + 2} \times \dfrac{6}{6} = \dfrac{-60}{18q + 12} $ Multiply the second expression by $\dfrac{3q + 2}{3q + 2}$ $ \dfrac{-7}{6} \times \dfrac{3q + 2}{3q + 2} = \dfrac{-21q - 14}{18q + 12} $ Therefore $ a = \dfrac{-60}{18q + 12} + \dfrac{-21q - 14}{18q + 12} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{-60 - 21q - 14}{18q + 12} $ $a = \dfrac{-21q - 74}{18q + 12}$